Envelope Detection

"Anonymous" <someone@microsoft.com> writes:
> [...]
> If I want to take the envelope of a signal I just mix it to baseband and ...

That's actually one step further than the HT - the HT provides the so-called
analytic signal. Mixing the analytic signal to baseband provides the equivalent
of your operation.
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Jerry Avins <jya@ieee.org> wrote in
news:j4CdnQ2WfeXFZLbZnZ2dnUVZ_tWdnZ2d@rcn.net: 

> Al Clark wrote:
> 
>    ...
> 
>> If I need a Hilbert transform that extends over a very large
>> frequency range, I use remez exchange to minimize the ripple. The
>> catch is that you don't get to throw out every other coefficient
>> since in general, all the coefficients are non zero. 
> 
> I concluded, from the few simulations I ran, that a filter with 
> alternate zeros, while longer than an optimized filter of the same 
> ripple, has fewer taps that need computing.* It isn't that multiplying
> by zero is easy; by marching through the data buffer with a stride of 
> two, the zeros might as well not exist. Windows that best remove
> ripple reduce bandwidth the most, requiring more taps to get it back.

I thought this might be the case. Maybe the window version is 1.5 x longer, 
but you skip the trivial zeros which still makes it a better choice.



> 
>> I think that sometimes people forget that it takes a very long filter
>> to create a 90 degree phase shift at low frequency. It's easy to
>> visualize why if you think about how to create a 90 degree phase
>> shift at DC. 
> 
> I've had a computer tied up since New Years calculating a filter to do
> that. :-) 

Must not have been a Windows machine. They don't operate long enough 
without a crash. It seems to me that a very long Digital FIR will also be 
constrained to a maximum size as the theoretical coefficients of the 
impulse response become too small to quantize for the given word size.

I calculated a hilbert FIR using a Kaiser Window with 2047 taps. The 
smallest tap was 12.76 x 10^-6 (0x00006B25). The sample rate was 96000 and 
the hilbert transform was good to about 80 Hz. After that the low 
frequencies start to roll off fast. If this was designed for wide band 
audio, I would probably need about 8000 taps (with 4000 non zero 
coefficents). 

> 
>> The other thing that I find is that in many cases I actually don't
>> need the envelope, I just need the mean squared (I^2 + Q^2) vs
>> SQRT(I^2 + Q^ 2). In a detector, I might just compare the result to
>> some arbitrary level. This means I can skip the SQRT.
> 
> I've seen programs that calculate the square root and then convert to 
> decibels. 

If they didn't also need the linear result, then I think they should go 
back and review basic 9th grade algebra.




> 
> Jerry
> ___________________________
> 

* "My mind is made up. Don't confuse me with facts"

Jerry, Are you commenting about our "fine" President? 

-- 
Al Clark
Danville Signal Processing, Inc.
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